Healing and relaxation in flows of Helium II. IV. Comparison with Khalatnikov-Lebedev theory

The three previous papers in this series have generalized Landau's two-fluid equations in the simplest possible way to include high-frequency and wavenumber effects, and have shown how the resulting theory may be applied, with at least one encouraging experimental confirmation. The present paper clarifies the relationship of the theory to a recently proposed alternative by Khalatnikov and Lebedev. The basic assumptions of their theory are exposed and a serious shortcoming (the implied irrotationality of the Saffman-Putterman vector) is discovered: a method of rectifying the difficulty is proposed. It is also shown how noncanonical transformations of their underlying canonical system can explain the presence of certain kinetic coefficients in their dissipative theory and ours. It is demonstrated that, in addition to the familiar contributions from the normal fluid and the superfluid, the momentum density in their theory in general contains a part parallel to the gradient in the modulus of the order parameter.